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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- UGC NET
- Economics
2 consider the following matrix which describes the respective strategies and the corresponding payoffs of firms a and b operating in a duopoly firm b advertise
2 Consider the following matrix which describes the respective strategies and the corresponding payoffs of firms A and B operating in a duopoly Firm B Advertise Don't Advertise Advertise 11,6 16, 0 Firm A Don't Advertise 7,9 20, 2 Which of the following statement(s) is/are true for the above game ? Select the correct answer from the codes given below (a) Firm A has no dominant strategy. (b) Firm B has a dominant strategy. (C) The game has a Nash equilibrium. (d) Neither Firm A nor Firm B has a dominant strategy. Code (1) (a), (c) (2) (b), (c) (3) (d) Only (4) (a), (b) and (c)
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Nidhi taparia Best Answer
The correct code is (4), because options a, b and c are correct. Let's see why. First of all please refer to the image to see the payoff matrices of each A and B firms. a is correct because Firm A does not have a dominant strategy. Because none of the strategies (advertise or not advertise) will for sure lead to a better result. Because elements of row 1 are neither all more or all less than elements of row 2. b is correct because Firm B does have a dominant strategy and that is to advertise. The elements of column 1 are all greater than column 2 in its matrix. c is correct because the Nash equilibrium does exist. Both firms will advertise, using row and col maximin approach respectively. This will lead to A gaining 11 and B gaining 6. Refer to the image for complete solutions.